Zero Coupon Bond

The investor's return is the difference between the purchase price and the face value — the accretion of the bond's value from its discounted purchase price to par over the holding period — rather than periodic cash income supplemented by a capital component as with coupon-bearing bonds. 

Zero coupon bonds are characterised by three defining investment characteristics that distinguish them from all coupon-bearing bonds — the complete elimination of reinvestment risk because there are no interim cash flows to reinvest, the highest interest rate sensitivity of any fixed income instrument of the same maturity because the entire economic value is concentrated in a single terminal payment making the duration equal to the time to maturity, and the phantom income tax problem that requires investors to pay annual income taxes on imputed interest that accrues each year without any corresponding cash receipt. 

Zero coupon bonds are tested on the Series 65 examination in the context of fixed income products, the elimination of reinvestment risk, the relationship between duration and interest rate sensitivity, and the OID phantom income tax treatment.

How Zero Coupon Bonds Are Created and Priced

Zero coupon bonds are created in two primary ways — direct issuance by the borrower as a zero coupon instrument, or the stripping of coupon payments from existing coupon-bearing Treasury bonds through the STRIPS programme to create synthetic zero coupon instruments from each individual cash flow.

Directly issued zero coupon bonds include United States Treasury bills — which are zero coupon instruments with maturities of one year or less sold at a discount to face value — and longer-term zero coupon bonds issued by corporations and municipalities. Treasury bills are the most widely held zero coupon instruments in the world and serve as the empirical proxy for the risk-free rate in financial theory.

Treasury STRIPS — Separate Trading of Registered Interest and Principal Securities — are created when primary dealers strip the coupon and principal payments of Treasury notes and bonds into individual zero coupon components, each of which trades as a separate zero coupon security with a specific maturity date corresponding to the date of that particular cash flow. A thirty-year Treasury bond has sixty semi-annual coupon payments plus one principal payment — stripped, these sixty-one cash flows become sixty-one separate zero coupon STRIPS with maturities ranging from six months to thirty years. The STRIPS programme is discussed in detail in the Treasury Bond and Treasury Note entries of this dictionary.

The pricing of a zero coupon bond follows directly from the present value formula — the price equals the face value divided by the quantity one plus the yield to maturity raised to the power of the number of periods to maturity.

Zero coupon bond price equals face value divided by the quantity one plus yield to maturity raised to the power of years to maturity.

A twenty-year zero coupon bond with a one thousand dollar face value and a yield to maturity of five percent is priced at one thousand divided by one point zero five raised to the twentieth power — equalling one thousand divided by two point six five three three — equalling approximately three hundred and seventy-seven dollars. An investor who pays three hundred and seventy-seven dollars today will receive one thousand dollars in twenty years — an annualised return of five percent over the full holding period.

The Elimination of Reinvestment Risk — The Defining Advantage

The most significant investment advantage of zero coupon bonds relative to coupon-bearing bonds of equivalent maturity is the complete elimination of reinvestment risk — the risk that coupon payments received during the bond's life will be reinvested at interest rates lower than the original yield to maturity, causing the realised total return to fall below the stated YTM.

As established in the Yield to Maturity entry of this dictionary, the YTM of a coupon-bearing bond assumes that every coupon payment is reinvested at the same rate as the YTM itself. This assumption is almost never perfectly realised in practice because interest rates change continuously — when rates fall, reinvested coupons earn less than assumed, reducing the realised return below the YTM.

A zero coupon bond has no interim coupon payments to reinvest. The entire return is determined at the moment of purchase by the relationship between the purchase price and the face value — and this return is locked in for the full holding period regardless of what happens to interest rates during the intervening years. An investor who purchases a twenty-year zero coupon bond at a yield of five percent today will receive a five percent annualised return on their investment in twenty years regardless of whether interest rates rise to ten percent or fall to one percent during the holding period. This mathematical certainty of the realised return — assuming no default — makes zero coupon bonds uniquely valuable for liability-driven investing strategies where a specific dollar amount must be available at a specific future date.

Pension funds and insurance companies use zero coupon bonds extensively for liability matching — purchasing a portfolio of zero coupon bonds maturing on the dates of specific known future liability payment obligations, ensuring that the assets available on each payment date precisely match the liability due on that date without any reinvestment risk.

The Maximum Duration — The Defining Risk

While zero coupon bonds eliminate reinvestment risk entirely, they amplify interest rate risk to the maximum possible level for any fixed income instrument of equivalent maturity. A zero coupon bond's duration — the primary measure of interest rate sensitivity — equals its time to maturity. A thirty-year zero coupon bond has a duration of thirty years — the highest duration of any bond maturing in thirty years.

The reason for this maximum duration is mathematical — duration measures the weighted average time to receipt of all cash flows. For a coupon-bearing bond, some cash flows are received before maturity in the form of coupon payments — these early cash flows reduce the weighted average time below the time to maturity. For a zero coupon bond, the only cash flow is received at maturity — the weighted average time to receipt of all cash flows equals the time to maturity exactly.

The practical consequence is that zero coupon bond prices are more sensitive to interest rate changes than any other fixed income instrument of the same maturity. A thirty-year zero coupon bond with a duration of thirty years will decline in price by approximately thirty percent if interest rates rise by one percentage point — a much larger decline than a thirty-year coupon-bearing bond with a duration of perhaps seventeen to nineteen years. As confirmed in the SEC's investor.gov description, zero coupon bond prices fluctuate more than other types of bonds in the secondary market precisely because of this extended duration.

This maximum interest rate sensitivity makes zero coupon bonds powerful instruments for investors who want maximum duration exposure — to benefit maximally from expected interest rate declines — but also makes them dangerous for investors who do not want to bear such extreme price volatility. An investor who must sell a zero coupon bond before maturity in a rising rate environment can suffer very large capital losses relative to the purchase price.

The Phantom Income Tax Problem — The Critical Tax Disadvantage

The most significant tax disadvantage of zero coupon bonds — and the feature most critical for investment advisers to understand and communicate to clients — is the Original Issue Discount tax treatment that requires investors to pay income taxes each year on imputed interest income that accrues but is never actually received as cash until maturity.

Under IRC Section 1272 and the Original Issue Discount rules, the discount at which a zero coupon bond is purchased is treated as taxable interest income that accrues ratably over the bond's life using the constant yield method — even though no cash interest payment is actually made. Each year, a portion of the total discount — the difference between the purchase price and the face value — is treated as ordinary income received by the investor and reported on Form 1099-OID, requiring the investor to pay federal income tax on that phantom income in the year it accrues.

An investor who purchases a twenty-year zero coupon bond for three hundred and seventy-seven dollars will ultimately receive one thousand dollars at maturity — a total discount of six hundred and twenty-three dollars spread over twenty years of tax obligations. Each year the investor receives a Form 1099-OID reporting the imputed interest that accrued during the year and owes income tax on that amount at their applicable marginal rate — without receiving any cash to fund the tax payment. This cash-flow-negative tax obligation — paying taxes on income that has not been received as cash — makes zero coupon bonds generally inappropriate for taxable accounts.

Zero coupon bonds are generally most appropriate for tax-deferred accounts — traditional IRAs, 401(k) plans, and other retirement accounts — where the annual OID accrual does not create a current tax liability because all growth in the account is tax-deferred until distribution. In a tax-deferred account the phantom income issue is entirely irrelevant because no taxes are owed until withdrawal regardless of the character of income generated within the account.

Municipal zero coupon bonds are an exception — the tax-exempt status of municipal bond interest under IRC Section 103 extends to the OID accrual on municipal zero coupon bonds, making them appropriate for taxable accounts for investors in high marginal tax brackets who want the certainty of a known future dollar amount without the phantom income tax obligation.

Common Uses of Zero Coupon Bonds

The unique combination of zero coupon bonds' investment characteristics — elimination of reinvestment risk, known terminal value, maximum duration, and phantom income — creates a specific set of investor applications for which zero coupon bonds are ideally suited.

College savings is a classic application — parents who know their child will need a specific sum in fifteen years can purchase zero coupon bonds maturing in fifteen years, ensuring the exact required amount will be available at the right time without any reinvestment risk from reinvesting interim coupon income. The FINRA investor education description notes specifically that zero coupon bonds are often purchased to meet a future expense such as college costs.

Retirement income planning uses zero coupon bonds to create certainty about future income — a retiree can purchase a ladder of zero coupon bonds maturing in successive years to provide a known annual income stream matching their spending needs without depending on interest rate conditions at the time of reinvestment.

Liability-driven investing for pension funds and insurance companies uses zero coupon bonds to match specific future liability payment dates — ensuring that the assets available on each date precisely equal the liability obligation due on that date, eliminating both reinvestment risk and interest rate risk for the matched portion of the liability.

Examination Relevance and Key Takeaways

Zero coupon bonds are tested on the Series 65 examination in the context of fixed income products, reinvestment risk elimination, duration and interest rate sensitivity, OID tax treatment, and appropriate use in taxable versus tax-deferred accounts.

The key points to retain are these.

A zero coupon bond pays no periodic interest — it is purchased at a discount to face value and redeems at full face value at maturity, with the discount representing the entire investment return. Zero coupon price equals face value divided by the quantity one plus YTM raised to the power of years to maturity. Treasury bills are zero coupon instruments with maturities of one year or less. Treasury STRIPS are synthetic zero coupon instruments created by stripping individual coupon and principal payments from Treasury notes and bonds.

The three defining characteristics are complete elimination of reinvestment risk — no interim coupons to reinvest means the YTM is guaranteed to be realised if held to maturity regardless of interest rate changes; maximum duration equal to time to maturity — a thirty-year zero coupon bond has duration of thirty years, producing approximately thirty percent price decline per one percentage point rise in yields — the highest interest rate sensitivity of any instrument of equivalent maturity; and phantom income OID tax treatment — IRC Section 1272 requires annual recognition and taxation of imputed interest income that accrues but is never received as cash, creating cash-flow-negative tax obligations that make zero coupon bonds generally inappropriate for taxable accounts.

Zero coupon bonds are generally most appropriate for tax-deferred retirement accounts where OID accrual creates no current tax liability, or for tax-exempt municipal zero coupon bonds in taxable accounts. Common uses include college savings funding, retirement income laddering, and institutional liability-driven investing for pension funds matching specific future payment obligations.